$A$ bullet fired into a fixed target loses half of its velocity after penetrating $1\,cm$. How much further will it penetrate before coming to rest,assuming that it faces constant resistance to motion?

$A$ tennis ball dropped from a height of $2 \,m$ rebounds only $1.5 \,m$ after hitting the ground. What fraction of its energy is lost in the impact?

$A$ bullet of mass $0.012\;kg$ and horizontal speed $70\;m\;s^{-1}$ strikes a block of wood of mass $0.4\;kg$ and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises. Also,estimate the amount of heat produced in the block.

$A$ rain drop of radius $2 \; mm$ falls from a height of $500 \; m$ above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height,it attains its maximum (terminal) speed,and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is $10 \; m s^{-1}$?

$A$ bullet of mass $30 \,g$ moving with $700 \,ms^{-1}$ collides with a block of mass $4 \,kg$ hanging by a string of length $0.4 \,m$. After the collision, the block rises to a height of $0.2 \,m$. Find the velocity of the bullet when it emerges from the block. (in $\,ms^{-1}$)

$A$ particle of mass $m$ is projected with a speed $u$ from the ground at an angle $\theta = \frac{\pi}{3}$ w.r.t. horizontal ($x$-axis). When it has reached its maximum height,it collides completely inelastically with another particle of the same mass and velocity $u \hat{i}$. The horizontal distance covered by the combined mass before reaching the ground is